In this work, we applied multiscale modeling to investigate electrical conductivity of carbon nanotube (CNT) enhanced polymer composites. The multiscale approach is based on a combination of first-principles calculations of contact resistance between CNTs using Green's functions approach and statistical calculation of CNTs ensemble conductivity using the Monte Carlo percolation model. The results of first-principles calculations show strong dependence of contact resistance between CNTs on the angle φ between nanotubes axes: for (5,5) CNTs contact resistance increases by two orders of magnitude as φ changes from φ=0 to φ=π/4. This angular dependence of contact resistance has strong influence on conductivity of CNTs ensemble, decreasing composite conductivity by about an order of magnitude. We stress that obtained conductivity is the upper theoretical limit for an ideal CNT composite, and experimental data with larger values of conductivity should be attributed to positive influence of some non-idealities in composite.

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